Terrence Howard to Cops: My Wife's Extorting Me, and I Have Her on Tape!

Terrence Howard filed a police report with the LAPD Monday, claiming his estranged wife is extorting him, and we're told he presented a shocking audio tape as proof.

Law enforcement sources tell TMZ ... Howard and his lawyer went to the LAPD to file the crime report. Howard claims Michelle Ghent Howard is squarely demanding money from him, in return for not making a Terrence sex tape and other embarrassing things public.

The former couple is in an epically bitter divorce battle. Among many things, Terrence claims Michelle is a racist who threatened to have him killed ... by the Russians.

The LAPD had no official comment, but we're told cops are in possession of the audio tape and they are investigating the extortion claim.